Algorithms for scheduling parallel batch processing machines with non-identical job ready times

This research is motivated by a practical application observed at a printed circuit board (PCB) manufacturing facility. After assembly, the PCBs (or jobs) are tested in environmental stress screening (ESS) chambers (or batch processing machines) to detect early failures. Several PCBs can be simultaneously tested as long as the total size of all the PCBs in the batch does not violate the chamber capacity. PCBs from different production lines arrive dynamically to a queue in front of a set of identical ESS chambers, where they are grouped into batches for testing. Each line delivers PCBs that vary in size and require different testing (or processing) times. Once a batch is formed, its processing time is the longest processing time among the PCBs in the batch, and its ready time is given by the PCB arriving last to the batch. ESS chambers are expensive and a bottleneck. Consequently, its makespan has to be minimized. ^ A mixed-integer formulation is proposed for the problem under study and compared to a formulation recently published. The proposed formulation is better in terms of the number of decision variables, linear constraints and run time. A procedure to compute the lower bound is proposed. For sparse problems (i.e. when job ready times are dispersed widely), the lower bounds are close to optimum. ^ The problem under study is NP-hard. Consequently, five heuristics, two metaheuristics (i.e. simulated annealing (SA) and greedy randomized adaptive search procedure (GRASP)), and a decomposition approach (i.e. column generation) are proposed—especially to solve problem instances which require prohibitively long run times when a commercial solver is used. Extensive experimental study was conducted to evaluate the different solution approaches based on the solution quality and run time. ^ The decomposition approach improved the lower bounds (or linear relaxation solution) of the mixed-integer formulation. At least one of the proposed heuristic outperforms the Modified Delay heuristic from the literature. For sparse problems, almost all the heuristics report a solution close to optimum. GRASP outperforms SA at a higher computational cost. The proposed approaches are viable to implement as the run time is very short. ^

Computer program for the analysis of non-prismatic beams

One of the major problems in the analysis of beams with Moment of Inertia varying along their length, is to find the Fixed End Moments, Stiffness, and Carry-Over Factors. In order to determine Fixed End Moments, it is necessary to consider the non-prismatic member as integrated by a large number of small sections with constant Moment of Inertia, and to find the M/EI values for each individual section. This process takes a lot of time from Designers and Structural Engineers. The object of this thesis is to design a computer program to simplify this repetitive process, obtaining rapidly and effectively the Final Moments and Shears in continuous non-prismatic Beams. For this purpose the Column Analogy and the Moment Distribution Methods of Professor Hardy Cross have been utilized as the principles toward the methodical computer solutions. The program has been specifically designed to analyze continuous beams of a maximum of four spans of any length, integrated by symmetrical members with rectangular cross sections and with rectilinear variation of the Moment of Inertia. Any load or combination of uniform and concentrated loads must be considered. Finally sample problems will be solved with the new Computer Program and with traditional systems, to determine the accuracy and applicability of the Program.